The demand for communication systems with higher capacities has pushed the common design approaches of WDM (wavelength-division-multiplexed) optical systems to their limits. (WDM optical systems are fully familiar to those of ordinary skill in the art.) A typical configuration of a point-to-point WDM system includes a number of optical transmitters, optical multiplexers, spans of transmission fiber, optical amplifiers (traditionally, erbium-doped fiber amplifiers, or EDFAs), dispersion compensating devices, optical demultiplexers, and a number of optical receivers. Unfortunately, the usable gain bandwidth for the optical amplifiers typically used in current systems, such as, for example, EDFAs, is limited and not very broad, and the distortion of the signal does not allow for transmission over very long optical transmission links. This has led to the investigation of alternate methods for amplification with greater broadband capabilities that allow for longer spacing in between amplification and longer transmission distances. Optical systems with such broadband capabilities are commonly referred to as DWDM (dense wavelength-division-multiplexed) systems.
It has long been known that stimulated Raman scattering, which is a well-known physical phenomenon, can be employed to build amplifiers to compensate for fiber loss in optical transmission systems. In particular, Raman amplification, which is fully familiar to those of ordinary skill in the art, advantageously uses the fiber itself as the amplification medium. Specifically, high-power (Raman) pump waves are launched into a silica fiber at a wavelength lower than that of the signal(s) to be amplified. Amplification then occurs when the pump wavelength gives up its energy to create new photons at the signal wavelength(s).
In recent years, there has been increased interest in the possible practical uses of Raman amplification techniques. There are at least two primary reasons for this renewed interest. First, the Raman effect has a very broad gain curve, which makes it very attractive for today's broadband DWDM systems, fully familiar to those of ordinary skill in the art. And second, Raman amplification typically requires pumps with outputs of several hundreds of milliwatts. Semiconductor pump lasers with such power outputs have only recently become available, and thus Raman amplification has now become practical.
FIG. 1, for example, shows a typical Raman gain curve, normalized so that the maximal gain is one, for a Raman pump operating at 205 THz (TeraHertz). Also shown is an illustrative set of channel frequencies in a typical state-of-the-art DWDM system. Illustratively, there are 128 channels, from 186.50 THz to 192.85 THz, with 50 GHz (GigaHertz) spacing between them. As can be seen from the figure, even a single Raman pump provides gain for a large part of the signal band.
Moreover, even broader Raman gain bandwidth can then be achieved by combining the Raman amplification effect of multiple pump waves selected carefully for the wavelength domain. FIG. 2, for example, shows an illustrative set of 6 Raman gain curves, each operating at a different frequency, which together provide gain throughout the entire desired signal band. Thus, by employing a small number (e.g., 6) of Raman pumps, each operating at a different frequency, it is possible to provide sufficient gain throughout the entire desired signal band.
As indicated above, Raman amplifiers for broadband systems typically employ multiple pumps. However, despite the advantages of Raman-pumped DWDM systems, there are some degradation effects which occur. For example, in addition to the desired pump-to-signal power transfer, there also exist pump-to-pump and signal-to-signal power transfers. These unwanted power transfers introduce gain tilting in such a way that signals at longer wavelengths may experience stronger gain than those at shorter wavelengths. This effect leads to non-uniform gain and thus the non-uniform linear penalty and noise level across the signal wavelengths. Additionally, power fluctuations over time within the Raman pump wave, which often occurs, may lead to amplified fluctuations or jitter, which also degrades system performance.
For at least these reasons, it has been recognized that it would be advantageous to adjust the powers of the pumps in Raman-pumped DWDM systems dynamically, so that signal powers are as flat as possible, relative to some given power target. One such recently developed technique for performing Raman pump power control to achieve such gain flattening is disclosed in U.S. Pat. No. 6,674,568, issued to X. Liu on Jan. 6, 2004 (hereinafter “Liu”), and commonly assigned to the assignee of the present invention. The technique of Liu uses a simple feedback mechanism based on the measured signal powers in order to adjust the pumps. More particularly, the Liu approach adapts the Raman pump powers (and, in certain embodiments thereof, the pump wavelengths as well), based on a closed-form mathematical formula which depends upon differences between a desired gain profile and a determined gain profile. U.S. Pat. No. 6,674,568 is hereby incorporated by reference as if fully set forth herein.
Note, however, that the technique as disclosed in Liu has certain limitations. First, it typically requires a number of feedback iterations for the pump settings to converge. Second, it can be determined that the effect of the Liu procedure is to approximately minimize the deviation of the signal powers from the target in a least-squares sense (i.e., to minimize the sum of the squares of the differences between the actual signal power at a given frequency and the target signal power at that frequency), even though it would be more advantageous to minimize the peak-to-peak ripple of the signal powers (i.e., to minimize the difference between the maximum difference between the actual signal power a given frequency and the target signal power at that frequency, and the minimum difference between the actual signal power at a given frequency and the target signal power at that frequency). In fact, it can be shown that the use of a least-squares minimization achieves a less desirable result than the use of a peak-to-peak ripple minimization, which difference may be potentially significant, especially as the number of signal channels increases. And third, when the number of channels exceeds the number of pumps (as is typical), there are channel configurations with arbitrary large ripple that lie in a certain null space of the least-squares formulation and thus cannot be corrected by the relatively simple feedback approach of Liu. Although it is possible to overcome the problem of slow convergence with a straightforward modification of the Liu technique, even after such a modification, the result nonetheless comprises a least-squares minimization approach.
In U.S. Pat. No. 6,912,084, issued to R. Freund on Jun. 28, 2005 (hereinafter, “Freund”) and commonly assigned to the assignee of the present invention, an improvement on the technique on of Liu is provided with use of a method and apparatus for controlling the pump powers of a broadband DWDM optical system using Raman amplification which determines pump settings that are advantageously directed to minimizing the peak-to-peak ripple of the channel powers with respect to a given per-channel target. More specifically, the method and apparatus disclosed in Freund first formulates a linear programming optimization problem, and then solves the formulated linear program in order to derive a new set of pump powers to be applied to the Raman amplification pumps. (As is well known to those skilled in the art, a linear programming optimization problem comprises an objective function to be optimized together with a set of constraints.) The optimization problem developed by the technique of Freund may then be solved with use of any conventional linear programming solution technique, such as, for example, the simplex method (which is fully familiar to those of ordinary skill in the art), thus providing Raman pump power settings to obtain an optimal gain profile. U.S. Pat. No. 6,912,084 is hereby incorporated by reference as if fully set forth herein.
However, a problem exists with the method of Freund in how the algorithm treats portions of the frequency spectrum which do not contain any active channels. The method disclosed in Freund simply ignores this region of the spectrum, and as such, changes to the Raman pumps can increase the amplification of this region of the spectrum leading to the growth of unwanted noise. Typically, this occurs because one of the Raman pumps has little or no impact on the active channels. Thus, the linear program of Freund can set this pump arbitrarily high since it will not change the gain at the active channels and thus will not change the value of the objective function. Unfortunately, this pump increase will impact the gain profile in the unoccupied channel region, resulting in amplification of background noise.
One method of combating this problem with the Freund method would be to add actual channels to this region of the spectrum. In this manner, the added channels enter the optimization problem and thus decrease the growth of noise. However, additional hardware, which can be quite expensive, would be required to light and maintain this power to these additional channels.